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Simplifying 25r2 + 40 = -20r Reorder the terms: 40 + 25r2 = -20r Solving 40 + 25r2 = -20r Solving for variable 'r'. Reorder the terms: 40 + 20r + 25r2 = -20r + 20r Combine like terms: -20r + 20r = 0 40 + 20r + 25r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + 4r + 5r2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + 4r + 5r2)' equal to zero and attempt to solve: Simplifying 8 + 4r + 5r2 = 0 Solving 8 + 4r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + 0.8r + r2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 0.8r + -1.6 + r2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 0.8r + r2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 0.8r + r2 = 0 + -1.6 0.8r + r2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 0.8r + r2 = -1.6 The r term is 0.8r. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8r + 0.16 + r2 = -1.6 + 0.16 Reorder the terms: 0.16 + 0.8r + r2 = -1.6 + 0.16 Combine like terms: -1.6 + 0.16 = -1.44 0.16 + 0.8r + r2 = -1.44 Factor a perfect square on the left side: (r + 0.4)(r + 0.4) = -1.44 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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